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Integral Representation (integral + representation)

Distribution by Scientific Domains
Mathematics and Statistics66%
Chemistry22%

Terms modified by Integral Representation

  • integral representation formula
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    Selected Abstracts

    Electromagnetic scattering by a perfectly conducting obstacle in a homogeneous chiral environment: solvability and low-frequency theory

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2002
    C. Athanasiadis
    Abstract The scattering of plane time-harmonic electromagnetic waves propagating in a homogeneous isotropic chiral environment by a bounded perfectly conducting obstacle is studied. The unique solvability of the arising exterior boundary value problem is established by a boundary integral method. Integral representations of the total exterior field, as well as of the left and right electric far-field patterns are derived. A low-frequency theory for the approximation of the solution to the above problem, and the derivation of the far-field patterns is also presented. Copyright © 2002 John Wiley & Sons, Ltd. [source]

    From the Hagedoorn imaging technique to Kirchhoff migration and inversion

    GEOPHYSICAL PROSPECTING, Issue 6 2001
    Norman Bleistein
    The seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique , a ,string construction' or ,ruler and compass' method , for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave-equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle-dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two. [source]

    Semigroup approach for identification of the unknown diffusion coefficient in a quasi-linear parabolic equation

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2007
    Ali Demir
    Abstract This article presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(u(x,t)) in the quasi-linear parabolic equation ut(x,t)=(k(u(x,t))ux(x,t))x, with Dirichlet boundary conditions u(0,t)=,0, u(1,t)=,1. The main purpose of this paper is to investigate the distinguishability of the input,output mappings ,[,]:,, ,C1[0,T], ,[,]:,,,C1[0,T] via semigroup theory. In this paper, it is shown that if the null space of the semigroup T(t) consists of only zero function, then the input,output mappings ,[,] and ,[,] have the distinguishability property. It is also shown that the types of the boundary conditions and the region on which the problem is defined play an important role in the distinguishability property of these mappings. Moreover, under the light of measured output data (boundary observations) f(t):=k(u(0,t))ux(0,t) or/and h(t):=k(u(1,t))ux(1,t), the values k(,0) and k(,1) of the unknown diffusion coefficient k(u(x,t)) at (x,t)=(0,0) and (x,t)=(1,0), respectively, can be determined explicitly. In addition to these, the values ku(,0) and ku(,1) of the unknown coefficient k(u(x,t)) at (x,t)=(0,0) and (x,t)=(1,0), respectively, are also determined via the input data. Furthermore, it is shown that measured output dataf(t) and h(t) can be determined analytically by an integral representation. Hence the input,output mappings ,[,]:,,, C1[0,T], ,[,]:,,,C1[0,T] are given explicitly in terms of the semigroup. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Weak solutions for time-dependent boundary integral equations associated with the bending of elastic plates under combined boundary data

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2004
    Igor Chudinovich
    Abstract The existence, uniqueness, stability, and integral representation of distributional solutions are investigated for the equations of motion of a thin elastic plate with a combination of displacement and moment-stress components prescribed on the boundary. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Introduction to a general crystallography

    ACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2001
    A. Janner
    The definition of an extended crystallographic group is given, based on an -dimensional Euclidean space, carrier of a faithful integral representation of a permutation group of atomic positions. The Euclidean crystallography of normal crystals and the higher-dimensional one applied to incommensurately modulated crystals, intergrowth crystals and quasicrystals are special cases of a general crystallography. The same is true for the multimetrical crystallographic characterization of ice and of snow crystals. This approach can also be applied to single molecules, leading to what may be denoted as molecular crystallography. It possibly allows non-trivial structural relations between atomic positions belonging to the asymmetric unit of the molecular point group to be obtained. Two simple molecules, polycyclic aromatic hydrocarbons, are treated as illustrative examples. [source]

    Auxiliary functions for molecular integrals with Slater-type orbitals.

    INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 9 2006

    Abstract Many types of molecular integrals involving Slater functions can be expressed, with the ,-function method in terms of sets of one-dimensional auxiliary integrals whose integrands contain two-range functions. After reviewing the properties of these functions (including recurrence relations, derivatives, integral representations, and series expansions), we carry out a detailed study of the auxiliary integrals aimed to facilitate both the formal and computational applications of the ,-function method. The usefulness of this study in formal applications is illustrated with an example. The high performance in numerical applications is proved by the development of a very efficient program for the calculation of two-center integrals with Slater functions corresponding to electrostatic potential, electric field, and electric field gradient. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source]

    Boundary integral equations for two-dimensional low Reynolds number flow past a porous body

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2009
    Mirela Kohr
    Abstract In this paper we use the method of matched asymptotic expansions in order to study the two-dimensional steady flow of a viscous incompressible fluid at low Reynolds number past a porous body of arbitrary shape. One assumes that the flow inside the porous body is described by the Brinkman model, i.e. by the continuity and Brinkman equations, and that the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. By considering some indirect boundary integral representations, the inner problems are reduced to uniquely solvable systems of Fredholm integral equations of the second kind in some Sobolev or Hölder spaces, while the outer problems are solved by using the singularity method. It is shown that the force exerted by the exterior flow on the porous body admits an asymptotic expansion with respect to low Reynolds number, whose terms depend on the solutions of the abovementioned system of boundary integral equations. In addition, the case of small permeability of the porous body is also treated. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Oseen coupling method for the exterior flow.

    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2004
    Part II: Well-posedness analysis
    Abstract In this paper, we recall the Oseen coupling method for solving the exterior unsteady Navier,Stokes equations with the non-homogeneous boundary conditions. Moreover, we derive the coupling variational formulation of the Oseen coupling problem by using of the integral representations of the solution of the Oseen equations at an infinity domain. Finally, we provide some properties of the integral operators over the artificial boundary and the well-posedness of the coupling variational formulation. Copyright © 2004 John Wiley & Sons, Ltd. [source]

    Construction of rigid local systems and integral representations of their sections

    MATHEMATISCHE NACHRICHTEN, Issue 3 2006
    Yoshishige Haraoka
    Abstract We give a method for constructing all rigid local systems of semi-simple type, which is different from the Katz,Dettweiler,Reiter algorithm. Our method follows from the construction of Fuchsian systems of differential equations with monodromy representations corresponding to such local systems, which give an explicit solution of the Riemann,Hilbert problem. Moreover, we show that every section of such local systems has an integral representation. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]